How to construct invalid variable percent confidence interval?

OK, here you go sweetheart :)

I'm not too sure what you mean when you say: "Construct a Invalid variable percent confidence interval for the population proportion."

SO I'm going to assume you want a 95% confidence interval just for clarity sake.

p = 308/416 = 0.74

σ = √ [p(1 - p) /n]

σ = √ ((0.74 × 0.26) /416)

σ = 0.022

Formula for a 95% confidence interval :

p - 1.96σ < μ < p + 1.96σ

Substituting in values gives :

0.74 - (1.96 × 0.022) < μ < 0.74 + (1.96 × 0.022)

0.697 < μ < 0.783

0.70 < μ < 0.78

So, the mean of the proportion lies somewhere between 0.70 as the lower bound and 0.78 as the upper bound.

The confidence interval calculated above has a width that is not too wide which we can conclude to be a very good estimate of the actual mean.

Hope this helps !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!